TY - JOUR
T1 - Symmetric rank-one method based on some modified secant conditions for unconstrained optimization
AU - Narushima, Yasushi
PY - 2011/12/1
Y1 - 2011/12/1
N2 - The symmetric rank-one (SR1) method is one of the well-known quasi-Newton methods, and many researchers have studied the SR1 method. On the other hand, to accelerate quasi-Newton methods, some researchers have proposed variants of the secant condition. In this paper, we propose SR1 methods based on some modified secant conditions. We analyze local behaviors of the methods. In order to establish the global convergence of the methods, we apply the trust region method to our methods.
AB - The symmetric rank-one (SR1) method is one of the well-known quasi-Newton methods, and many researchers have studied the SR1 method. On the other hand, to accelerate quasi-Newton methods, some researchers have proposed variants of the secant condition. In this paper, we propose SR1 methods based on some modified secant conditions. We analyze local behaviors of the methods. In order to establish the global convergence of the methods, we apply the trust region method to our methods.
KW - Local convergence
KW - Modified secant conditions
KW - Symmetric rank-one method
KW - Trust region method
KW - Unconstrained optimization
UR - http://www.scopus.com/inward/record.url?scp=84879129190&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84879129190&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84879129190
SN - 0916-5746
VL - 47
SP - 25
EP - 43
JO - SUT Journal of Mathematics
JF - SUT Journal of Mathematics
IS - 1
ER -